Squares in arithmetic progression over number fields

Details Squares in arithmetic progression over number fields Squares in arithmetic progression over number fields

2009-09-09

arxiv.org/abs/0909.1642v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

We show that there exists an upper bound for the number of squares in
arithmetic progression over a number field that depends only on the degree of
the field. We show that this bound is 5 for quadratic fields, and also that the
result generalizes to $k$-powers for $k>1$.

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